# Gas Dynamics Equations

**URL:** <https://fenicsproject.discourse.group/t/gas-dynamics-equations/7159>\
**Category:** variational formulation\
**Created:** [November 23, 2021, 9:12pm UTC](https://fenicsproject.discourse.group/t/gas-dynamics-equations/7159 "2021-11-23T21:12:18Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Rania\_Abid](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/rania_abid/32/3223_2.png) [@Rania\_Abid](https://fenicsproject.discourse.group/u/Rania_Abid)\
**Post date:** [November 23, 2021, 9:12pm UTC](https://fenicsproject.discourse.group/t/gas-dynamics-equations/7159/1 "2021-11-23T21:12:18Z")

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Hello,  
I am trying to implement gas dynamics equations to describe the air heating and expansion due to the passage of the electrical current through the stem’s cross section.

![Capture1](https://global.discourse-cdn.com/free1/uploads/fenicsproject1/original/2X/0/0ba66b0e04b24fce0103e5eba6d01f725685f7e2.png)

The equation (1) accounts for mass transport.  
The equation (2) describes the transport of momentum.  
Equations (3) and (4) describe the energy transport.

Here’s the link for a full description: [http://membership.agu.org/files/2014/01/da-Silva-and-Pasko-2013-Dynamics-of-streamer-to-leader-transition-at-reduced-air-densities-and-its-implications-for-propagation-of-lightning-leaders-and-gigantic-jets.pdf](http://membership.agu.org/files/2014/01/da-Silva-and-Pasko-2013-Dynamics-of-streamer-to-leader-transition-at-reduced-air-densities-and-its-implications-for-propagation-of-lightning-leaders-and-gigantic-jets.pdf)

I couldn’t find similar topics and I’m struggling to find weak forms for these equations and to implement the model.  
May anyone help me with this?

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<div class="post-metadata">

**Author:** ![nate](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/nate/32/17_2.png) [@nate](https://fenicsproject.discourse.group/u/nate)\
**Post date:** [November 23, 2021, 9:22pm UTC](https://fenicsproject.discourse.group/t/gas-dynamics-equations/7159/2 "2021-11-23T21:22:48Z")

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Compressible flows are challenging. Consider looking into discretisations of the compressible Euler and compressible Navier-Stokes systems as a basis for your desired formulation. These are likely more extensively covered in the literature.

E.g: [Solving Compressible Flow Navier Stokes](https://fenicsproject.discourse.group/t/solving-compressible-flow-navier-stokes/3472)

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<div class="post-metadata">

**Author:** ![Rania\_Abid](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/rania_abid/32/3223_2.png) [@Rania\_Abid](https://fenicsproject.discourse.group/u/Rania_Abid)\
**Post date:** [November 23, 2021, 9:55pm UTC](https://fenicsproject.discourse.group/t/gas-dynamics-equations/7159/3 "2021-11-23T21:55:13Z")

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Thank you for your response.  
I already made researches on Navier-Stokes systems and I also implemented Gallimberti simplified model but it didn’t help much.  
I will consider reading more about these topics anyway, thanks!